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Oshanin, G., Vasilyev, O., Krapivsky, P. L., Klafter, J.
Survival of an evasive preyProceedings of the National Academy of Sciences of the United States of America, 106(33):13696-13701, 2009 (article)

Computational models of the neuromuscular system hold the potential to allow us to reach a deeper understanding of neuromuscular function and clinical rehabilitation by complementing experimentation. By serving as a means to distill and explore specific hypotheses, computational models emerge from prior experimental data and motivate future experimental work. Here we review computational tools used to understand neuromuscular function including musculoskeletal modeling, machine learning, control theory, and statistical model analysis. We conclude that these tools, when used in combination, have the potential to further our understanding of neuromuscular function by serving as a rigorous means to test scientific hypotheses in ways that complement and leverage experimental data.

Abstract The paper presents a two-layered system for (1) learning and encoding a periodic signal without any knowledge on its frequency and waveform, and (2) modulating the learned periodic trajectory in response to external events. The system is used to learn periodic tasks on a humanoid HOAP-2 robot. The first layer of the system is a dynamical system responsible for extracting the fundamental frequency of the input signal, based on adaptive frequency oscillators. The second layer is a dynamical system responsible for learning of the waveform based on a built-in learning algorithm. By combining the two dynamical systems into one system we can rapidly teach new trajectories to robots without any knowledge of the frequency of the demonstration signal. The system extracts and learns only one period of the demonstration signal. Furthermore, the trajectories are robust to perturbations and can be modulated to cope with a dynamic environment. The system is computationally inexpensive, works on-line for any periodic signal, requires no additional signal processing to determine the frequency of the input signal and can be applied in parallel to multiple dimensions. Additionally, it can adapt to changes in frequency and shape, e.g. to non-stationary signals, such as hand-generated signals and human demonstrations.

Locally-weighted regression is a computationally-efficient technique for non-linear regression.
However, for high-dimensional data, this technique becomes numerically brittle and computationally
too expensive if many local models need to be maintained simultaneously. Thus, local linear
dimensionality reduction combined with locally-weighted regression seems to be a promising solution.
In this context, we review linear dimensionality-reduction methods, compare their performance on nonparametric
locally-linear regression, and discuss their ability to extend to incremental learning. The
considered methods belong to the following three groups: (1) reducing dimensionality only on the input
data, (2) modeling the joint input-output data distribution, and (3) optimizing the correlation between
projection directions and output data. Group 1 contains principal component regression (PCR); group
2 contains principal component analysis (PCA) in joint input and output space, factor analysis, and
probabilistic PCA; and group 3 contains reduced rank regression (RRR) and partial least squares
(PLS) regression. Among the tested methods, only group 3 managed to achieve robust performance
even for a non-optimal number of components (factors or projection directions). In contrast, group 1
and 2 failed for fewer components since these methods rely on the correct estimate of the true intrinsic
dimensionality. In group 3, PLS is the only method for which a computationally-efficient incremental
implementation exists. Thus, PLS appears to be ideally suited as a building block for a locally-weighted
regressor in which projection directions are incrementally added on the fly.

Recent experimental and theoretical work [1] investigated the neural control of contact transition between motion and force during tapping with the index finger as a nonlinear optimization problem. Such transitions from motion to well-directed contact force are a fundamental part of dexterous manipulation. There are 3 alternative hypotheses of how this transition could be accomplished by the nervous system as a function of changes in direction and magnitude of the torque vector controlling the finger. These hypotheses are 1) an initial change in direction with a subsequent change in magnitude of the torque vector; 2) an initial change in magnitude with a subsequent directional change of the torque vector; and 3) a simultaneous and proportionally equal change of both direction and magnitude of the torque vector. Experimental work in [2] shows that the nervous system selects the first strategy, and in [1] we suggest that this may in fact be the optimal strategy. In [4] the framework of Iterative Linear Quadratic Optimal Regulator (ILQR) was extended to incorporate motion and force control. However, our prior simulation work assumed direct and instantaneous control of joint torques, which ignores the known delays and filtering properties of skeletal muscle.
In this study, we implement an ILQR controller for a more biologically plausible biomechanical model of the index finger than [4], and add activation-contraction dynamics to the system to simulate muscle function. The planar biomechanical model includes the kinematics of the 3 joints while the applied torques are driven by activation?contraction dynamics with biologically plausible time constants [3]. In agreement with our experimental work [2], the task is to, within 500 ms, move the finger from a given resting configuration to target configuration with a desired terminal velocity. ILQR does not only stabilize the finger dynamics according to the objective function, but it also generates smooth joint space trajectories with minimal tuning and without an a-priori initial control policy (which is difficult to find for highly dimensional biomechanical systems).
Furthemore, the use of this optimal control framework and the addition of activation-contraction dynamics considers the full nonlinear dynamics of the index finger and produces a sequence of postures which are compatible with experimental motion data [2]. These simulations combined with prior experimental results suggest that optimal control is a strong candidate for the generation of finger movements prior to abrupt motion-to-force transitions.
This work is funded in part by grants NIH R01 0505520 and NSF EFRI-0836042 to Dr. Francisco J. Valero- Cuevas
1 Venkadesan M, Valero-Cuevas FJ. Effects of neuromuscular lags on controlling contact transitions. Philosophical Transactions of the Royal Society A: 2008.
2 Venkadesan M, Valero-Cuevas FJ. Neural Control of Motion-to-Force Transitions with the Fingertip. J. Neurosci., Feb 2008; 28: 1366 - 1373;
3 Zajac. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit Rev Biomed Eng, 17
4. Weiwei Li., Francisco Valero Cuevas: ?Linear Quadratic Optimal Control of Contact Transition with Fingertip ? ACC 2009

Abstract The paper presents a two-layered system for (1) learning and encoding a periodic signal without any knowledge on its frequency and waveform, and (2) modulating the learned periodic trajectory in response to external events. The system is used to learn periodic tasks on a humanoid HOAP-2 robot. The first layer of the system is a dynamical system responsible for extracting the fundamental frequency of the input signal, based on adaptive frequency oscillators. The second layer is a dynamical system responsible for learning of the waveform based on a built-in learning algorithm. By combining the two dynamical systems into one system we can rapidly teach new trajectories to robots without any knowledge of the frequency of the demonstration signal. The system extracts and learns only one period of the demonstration signal. Furthermore, the trajectories are robust to perturbations and can be modulated to cope with a dynamic environment. The system is computationally inexpensive, works on-line for any periodic signal, requires no additional signal processing to determine the frequency of the input signal and can be applied in parallel to multiple dimensions. Additionally, it can adapt to changes in frequency and shape, e.g. to non-stationary signals, such as hand-generated signals and human demonstrations.

Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems